Question: Solve for $x$ and $y$ using elimination. ${-2x-2y = -22}$ ${-5x+2y = -48}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-7x = -70$ $\dfrac{-7x}{{-7}} = \dfrac{-70}{{-7}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-2x-2y = -22}\thinspace$ to find $y$ ${-2}{(10)}{ - 2y = -22}$ $-20-2y = -22$ $-20{+20} - 2y = -22{+20}$ $-2y = -2$ $\dfrac{-2y}{{-2}} = \dfrac{-2}{{-2}}$ ${y = 1}$ You can also plug ${x = 10}$ into $\thinspace {-5x+2y = -48}\thinspace$ and get the same answer for $y$ : ${-5}{(10)}{ + 2y = -48}$ ${y = 1}$